16.1.3 Strong Transworld Identity and mere haecceitistic differences
Suppose one thinks, with Plantinga, that Counterpart Theory is problematic because it entails the falsity of Strong Transworld Identity. Some have objected that this sort of view entails that there are “haecceitistic differences” between worlds. Two worlds are merely haecceitistically different if and only if they differ only with respect to the identities of objects in the two worlds, and not in any qualitative way.5 Consider, for example, a world w exactly like the actual world but where RCK and THP have switched roles. In w, RCK has all of THP's characteristics, and THP has all of RCK's characteristics, whether physical or psychological or otherwise. The only difference between w and the actual world concern identities. Qualitatively, the two worlds are exactly similar. (A commitment to mere haecceitistic differences between worlds does not entail a commitment to the existence of haecceities Def D9.2, nor does a commitment to the existence of haecceities entail a commitment to mere haecceitistic differences between worlds. We leave it as an exercise for the reader to work out why this is so. See Lewis 1986a.)
Some have argued that Strong Transworld Identity entails that some worlds are merely haecceitistically different (see Chisholm 1967 and Forbes 1985, for example; for a helpful overview of these arguments, see Mackie and Jago 2013). The arguments often rely on a series of thought experiments where small changes are strung together to make large changes, though no such series is necessary. Maybe, for example, one might initially think that a world where RCK and THP completely switch roles is not plausibly possible. However, it is quite plausible that RCK and THP could have exchanged a small subset of their qualitative features. For example, imagine a world w′ in which RCK is a couple inches taller and THP a couple inches shorter; that is, imagine that RCK and THP exchanged merely their respective heights. If that is possible, then certainly they could also exchange their respective hair colors; this is w″. And shoe sizes; w′″. And so on. Soon enough, they seem to have switched all of their physical features. Now continue this step-wise process with psychological changes, and so on. At no point in the sequence of worlds is there a place where it seems there is a principled way to deny that the switching is possible. (Imagination as Guide to Possibility PEpist 1 and patchwork principles PMeta 5 are at work here.) Therefore, Strong Transworld Identity, together with the claim that some ordinary objects have accidental properties, seems to entail the possibility of mere haecceitisitic differences between worlds.
Why are mere haecceitistic differences problematic? Return to w, in which RCK and THP have completely switched roles. One might puzzle at the idea that, in that world, THP is identical to the object that has all of the properties actually possessed by RCK. What sense can be made of the claim that it's THP that has those properties, according to that world? If that world were actual, the RCK-role filler would have none of the properties that THP actually has. It is, therefore, difficult to see how that object could be literally identical to THP. Mere haecceitistic differences, therefore, can seem incompatible with putative claims to Transworld Identity that they were meant to describe!
Defenders of Strong Transworld Identity ought to deny that mere haecceitistic differences between worlds are problematic in this way. To execute this strategy, they must blunt the force of the thought that radical role-switching is incompatible with Transworld Identity. There are two ways of reading the objection. On a metaphysical reading, the problem is supposed to be that there is nothing to ground the identity of THP as THP in w. But this is not obviously true. We built the role-switching thought experiment, and indeed the idea of mere haecceitistic differences, in terms of qualitative features. One might, therefore, think that there are non-qualitative features of objects that will not be switched in cases of mere haecceitistic differences. For example, Scotists (9.2A.2) could insist that had w been actual, THP would have still exemplified the haecceity that he actually exemplifies, despite the radical qualitative role-switching. More generally, one's solution to the problem of individuation discussed in Section 9.3.2 will impact the way one will deal with the present problem. That is, for each proposed solution to the problem of individuation, there will be a corresponding solution to this problem, whether in terms of haecceities, primitive identities, bare particulars, or whatever.6
There is, however, an epistemological reading of the worry. The concern is not that there is nothing to ground transworld identities, but rather that we have no way to know that w represents THP, rather than some other object, as occupying the RCK role. Kripke (1980) responds to this objection by insisting that, for Abstractionists, possible worlds are “not discovered by powerful telescopes” (p. 44, emphasis in original). Rather, by setting out to consider the possible world where THP and RCK switch roles, we thereby come to think about w, that world wherein THP and RCK have switched roles (if such there be). In that sense, according to Kripke (and others), there is really no epistemological problem here at all. Anyway, there is no epistemological problem beyond the more general problem of our knowledge of modality. We consider certain aspects of that problem in the Section 16.2.
16.1.4 Summary
Summarizing, there are six basic questions for every theory of modality:
What sorts of things are possibilities or possible worlds? What are they like? Are there impossible worlds as well?
What makes a world possible? What accounts for the existence and variety of possible worlds?
What makes the actual world actual? What is actuality?
How do worlds represent things being a certain way? What is it for something to be true according to a world?
How do worlds represent de re possibilities (possibilities of or for particular things)? Do particular things exist in more than one world?
How do we know that possible worlds of certain kinds do or do not exist?
Here's a table summarizing the possible answers to these questions on behalf of Concretists and Abstractionists:
Table 16.1 Comparing Concretism and Abstractionism
Concretism Abstractionism
1. Concrete, parallel universes Sets of propositions
States of affairs
Properties of the world (maximal structural universals)
2. Brute fact of existence Primitive property of possibility
(Combinatorialists) Mathematical facts about combinations
3. Location (indexicality) Primitive property of actuality
Facts about truth simpliciter
Facts about existence simpliciter
Facts about fundamentality
4. Literally contains a truthmaker for p Magical representation
Linguistic representation
Pictorial representation
5. Overlapping worlds
Counterpart relations between Worldbound Individuals
Russellian propositions (literally containing the thing)
Plantingan propositions (containing the haecceity of the thing)
6. Pure reason
Best theory for metaphysical data
Platonic vision of abstracta (a priori conceivability)
Empirical knowledge of the powers and potentialities of actual things
16.2 Modality and Epistemology: Possibility and Conceivability
We have canvassed a number of views about the nature of possible worlds, and about how possible worlds relate to modal facts. We have set aside epistemological issues for the most part, but the time has come to turn in that direction. There are number of questions with which philosophers wrestle regarding the relationship between modality and epistemology. We touch on just one here, namely the relationship between what is conceivable and what is possible. As we have seen in many cases, there is some sort of connection between what is conceivable and what is possible. Conceivability seems to be a fairly reliable source of information about what is possible. This is Imagination as Guide to Possibility, introduced in Chapter 3 and mentioned in a number of places thereafter:
PEp
ist 1 Imagination as Guide to Possibility. If a scenario is imaginable in great detail without evident absurdity, then we have good reason to think that it represents a metaphysical possibility.
One explanation of the truth of Imagination as Guide to Possibility is to suppose that possibility just is conceivability. If so, then every conceivable scenario is also really possible.
16.2T Conceivability Entails Possibility. Every conceivable scenario is true in some possible world.
There's an obvious problem with the suggestion, stronger than Conceivability Entails Possibility, that possibility just is conceivability. If this is supposed to ground possibility in something non-modal, then it can't work, since conceivability is already modal in character (as the suffix ‘-ability’ indicates). Something is conceivable just in case it is possibly conceived of, or more precisely, possible to conceive of when one's faculties are in good working order. As a reductive account of possibility, this would be viciously circular.
However, one might take Conceivability Entails Possibility to be, not a reduction or definition of possibility, but merely an assertion of the nature and scope of what possible worlds represent. On this reading, Conceivability Entails Possibility asserts that there are enough possible worlds and of sufficient variety to verify every conceivable scenario. Alternatively, it asserts that our ability to conceive things is somehow constrained by the possible worlds there are, so we can't conceive of the impossible. If this view is right, then the fact that a situation is conceivable is infallible evidence of possibility.
16.2.1 Various notions of conceivability
Before we evaluate Conceivability Entails Possibility, we must get a great deal clearer about the nature of conceivability. In fact, philosophers have identified a number of varieties of conceivability (see, especially, Chalmers 2002). Here are two:
Def D16.1.1 Negative epistemic conceivability. The hypothesis that p is negative-epistemic conceivable if and only if it is not knowable a priori that p is false.
Def D16.1.2 Positive-modal conceivability. The hypothesis that p is positive-modal conceivable if and only if it is knowable a priori that p is possible.
There are two cross-cutting distinctions here: negative vs. positive and epistemic vs. modal. Negative conceivability involves not being in a position to know that something is either false or impossible, while positive conceivability involves knowing that something is possible. Something is negative-epistemically conceivable if it's impossible to know that it is actually false.
It is trivial that positive-modal conceivability entails possibility, since knowledge entails truth. However, it is not trivial that possibility entails positive-modal conceivability. To accept the converse implication is to hold that what we can't know to be possible must be impossible.
The most plausible and interesting version of Conceivability Entails Possibility incorporates negative-epistemic conceivability:
16.2T.1 Lack of A Priori Falsity Entails Possibility. Every negative-epistemic conceivable scenario is true in some possible world.
Lack of A Priori Falsity Entails Possibility has been a popular thesis in the history of philosophy, especially in the modern period of Descartes, Locke, Hume, and Leibniz. Nonetheless, the thesis forces us to ask why we ought to suppose that there is any connection at all between a priori knowability and possibility. A priori knowability is an epistemological property of propositions; it concerns how we know that a proposition is actually true. Possibility is a metaphysical property; it concerns whether the proposition could be true, regardless of whether we know or could know that it is actually false. Lack of A Priori Falsity Entails Possibility is logically equivalent to its contraposition, Necessity Entails A Priori Knowability:
16.3T Necessity Entails A Priori Knowability. If p is necessarily true, then we can know a priori that p is true in fact.7
The converse of Necessity Entails A Priori Knowability, A Priori Knowability Entails Necessity, is perhaps more defensible:
16.4T A Priori Knowability Entails Necessity. If it is knowable a priori that p is false, then p is true in no possible world.
One might think that if we could know a priori that some proposition p is false, it must be impossible for p to be true. If p were possibly true, how could we know that it is false without consulting some kind of empirical data?
At any rate, if both of these principles are true, then necessity is equivalent to a priori knowability: a proposition would be necessary if and only if it is a priori knowable.
16.2.2 Objections to identifying the necessary and the a priori
Recent philosophy of language, beginning with the seminal work of Saul Kripke (1980), has raised powerful objections to the supposed correspondence between what is necessary and what can be known a priori. There are apparent counterexamples in both directions. There are claims that are contingent (not necessary) but knowable a priori, and other claims that are necessary but knowable only a posteriori.
THE CONTINGENT A PRIORI Propositions expressed by the following sentences are contingent:
(4) The standard meter stick is one meter long.
(5) I am here now.
(6) I exist.
Let's consider these in reverse order. If any modal claim is certain for us, then the claim that (6) is contingent is among them: I might never have existed. Simple as that. It would be the height of hubris for any of us to claim that we are necessary beings. Likewise for (5), uttered by THP at midday on 27 October 2015. THP certainly might have been located somewhere else at the time of that utterance. For example, had he decided to work on this chapter somewhere else than a particular coffee shop in Fullerton, California, (5) would have been false. Instead of being here, at Green Bliss in Fullerton, he could have been at home or in his office at Biola University.
What about (4), which seems a bit more controversial? There used to be a standard meter stick in Paris, and that particular piece of metal could have been shorter or longer than it was. Nothing guaranteed that it should be exactly as long as it was in fact. Had it been longer or shorter, though, it would have been longer or shorter than that length we now pick out by the phrase ‘one meter long’. To say that the standard meter stick is necessarily one meter long is to say something true read one way and false read another. The sentence, ‘The standard meter stick is one meter long’, is necessarily true understood de dicto. But the stick itself, considered as a particular bar of metal, could be beaten into any number of lengths, longer or shorter than a meter. The claim is, therefore, contingent understood de re.
Despite that each of (4), (5), and (6) are contingent, it seems that we can know them in a purely a priori way, without doing any observing, experimentation, or collection of empirical data. One doesn't need to do any observing to know that one exists, and one doesn't have to observe any facts about one's present location in order to know that one is “here”. Similarly, the concept of the standard meter stick seems to guarantee, apart from any a posteriori investigation, that the standard meter stick is in fact a meter long, even if that very stick might have been shorter or longer.
Immanuel Kant, who discovered the distinction between a priori and a posteriori knowledge as we now understand it, thought that (7) and (8) were also knowable a priori.
(7) There is a linear temporal order.
(8) Space is approximately Euclidean.
Kant thought that all possible human experience involved linear time and Euclidean space. Consequently, we don't have to consult empirical science to learn that the world we encounter in experience satisfies (7) and (8). Nonetheless, both (7) and (8) seem to be contingent. We could imagine a world in which they fail, even if such a world would be one that we human beings could not possibly experience through sense perception.
At any rate, if any of (4) through (8) are indeed examples of the contingent a priori, then A Priori Knowability Entails Necessity is false.
THE NECESSARY A POSTERIORI Even more pertinently, Kripke argued that many necessary truths canno
t be known a priori. Consider the following three identity claims:
(9) Mark Twain is Samuel Clemens.
(10) Water is H2O.
(11) Heat is mean kinetic energy.
Each of these identities were learned through empirical investigation. There is nothing about the concepts of Mark Twain, water, or heat that guarantee the truths of the propositions. Nonetheless, as we have seen, Kripke offered a powerful argument for thinking that all identities are necessarily true. There is no possible world in which Mark Twain is not Samuel Clemens, since that would have to be a world in which Mark Twain is not Mark Twain, since Mark Twain just is Samuel Clemens. Since there is just one thing here, everything true of the “one” is true of the “other”. It's impossible for Mark Twain not to be Mark Twain, so it must similarly be impossible for Mark Twain not to be Samuel Clemens. Similar remarks apply to (10) and (11). If any of (9) through (11) are examples of the necessary a posteriori, then Necessity Entails A Priori Knowability is false.
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